0 votes 0 votes State True or False? Empty set Φ is an equivalence relation. Set Theory & Algebra relations + – srestha asked Sep 21, 2018 srestha 1.9k views answer comment Share Follow See all 7 Comments See all 7 7 Comments reply Shaik Masthan commented Sep 21, 2018 reply Follow Share on which set you are applying this relation? if the set is non-empty, then it is trivial to say false but what is the answer, if the set is EMPTY? check this https://gateoverflow.in/229165/self-doubt 1 votes 1 votes srestha commented Sep 21, 2018 reply Follow Share given that it will be irreflexive but here https://math.stackexchange.com/questions/1203676/is-an-empty-set-reflexive-symmetric-transitive it is given that empty set contain equivalence relation 0 votes 0 votes Deepanshu commented Sep 21, 2018 reply Follow Share ANY SET OF ELEMENTS??? GIVEN OVER THAT RELATION IS TO BE FORMED 0 votes 0 votes Sayan Bose commented Sep 21, 2018 reply Follow Share Yes right as Shaik Masthan said that if the relation is formed from a non-empty set, then empty set is not an equivalence relation as the smallest equivalence relation must contain the diagonal elements i.e. (a,a);(b,b) and so on 0 votes 0 votes Deepanshu commented Sep 21, 2018 reply Follow Share @Sayan Bose SO IF SET IS EMPTY THEN I AM NOT ABLE TO DRAW CONCLUSION FROM https://gateoverflow.in/229165/self-doubt 0 votes 0 votes Sayan Bose commented Sep 21, 2018 reply Follow Share Yes I have seen the discussion on that link. Which part are you not able to understand ? 0 votes 0 votes Deepanshu commented Sep 21, 2018 reply Follow Share THAT PICTURE IS NOT LOADING AT THAT TIME. FROM PICTURE I UNDERSTAND :) 0 votes 0 votes Please log in or register to add a comment.
Best answer 2 votes 2 votes There is one thing relationship Empty relation on empty set is reflexive,irreflexive, symmetry, assymetric, antisymmetric and transtive Empty relation on non empty set is irreflexive, symmetry, asymmetric, antisymmetric, transtive. Tesla! answered Sep 21, 2018 • selected Jan 25, 2019 by Shaik Masthan Tesla! comment Share Follow See all 5 Comments See all 5 5 Comments reply Show 2 previous comments arvin commented Sep 22, 2018 reply Follow Share short and simple :) 0 votes 0 votes sripo commented Oct 10, 2018 reply Follow Share Can a relation be both reflexive and irreflexive.If yes can you please give examples.Aren't reflexive and irreflexive both mutually exclusive sets? 0 votes 0 votes Tesla! commented Oct 10, 2018 reply Follow Share @sripo Empty relation on empty set or both reflexive and irreflexive, it's only example I know , and you will find many material where proof is given 0 votes 0 votes Please log in or register to add a comment.